A torque graph can reverse a rotor

A rotor with constant inertia 2 kg·m² starts with angular velocity −2 rad/s. Its net torque rises linearly from zero at t=0 to +6 N·m at t=2 s, then falls linearly to zero at t=4 s.

Straight segments connect the net-torque observations.
t / s	τ / N·m
0	0
2	6
4	0

What is its angular velocity at t=4 s?

Organize the givens & assumptions

Inertia: 2 kg·m²
Initial angular velocity: −2 rad/s
Net torque triangle: base 4 s, height 6 N·m

Fixed rotation axis and constant inertia; the plotted torque is the complete external torque about that axis.

A $+4\ \mathrm{rad/s}$
B $+6\ \mathrm{rad/s}$
C $+10\ \mathrm{rad/s}$
D $-4\ \mathrm{rad/s}$

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